You may not be used to your new home for a while after your moving company
delivers your belongings, so it is important to try and adjust slowly. This is especially true for safety purposes, as you may still be used to your old home, and this could risk injury. When dealing with a new staircase, this issue may be even more important, whether just getting used to the stairs, or moving quickly due to an emergency or a hurry.
It may be a good idea to ensure that the stairs have sturdy railings on both sides. This may seem like too much, but one railing, or two that are not particularly strong, could prove dangerous. It is very possible that you will slip at one point traveling up or down on the stairs, and having strong railings will help you keep your balance and possibly prevent injury.
Another good idea could be to add carpeting to the stairs. This will increase the friction on the stairs, which may be necessary to cut down slipping, especially if you need to move quickly. There are many different types of carpeting available, and some may not only increase traction, but could also add positively to your room's look.
When traveling on the stairs, it may be a good idea to wear shoes. This will give you the best traction, as your shoes will grip the surface of the stairs more easily than your feet can. Additionally, avoiding using sandals or socks on the stairs is also a good idea. Neither of these options provide as good traction as shoes would, and you will be better off for using more durable footwear.